What is the Golden Ratio?
2 answers:
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Answer:
θ = 0.77+6.28k, -0.77+6.28k, includes {-7.05, -5.52, -0.77, 0.77, 5.52, 7.05}
Step-by-step explanation:
The principal value of θ can be found using the inverse cosine function:
θ = arccos(0.72) ≈ 0.766994
Additional values of θ that also satisfy the equation are values that are this far away from any multiple of 2π, that is, ...
θ = ±arccos(0.72) + 2kπ ≈ ±0.77 +6.28k
Some approximate values for θ are {-7.05, -5.52, -0.77, 0.77, 5.52, 7.05}.
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<em>Comment on multiples of π</em>
Since π is irrational, the larger the multiple, the larger the error for any given approximation of π. One needs to be careful to use a suitable approximation for the multiple of interest. The same problem affects calculator accuracy for angles of very large magnitude.
